A Brief Introduction to the Ekpyrotic Universe
Paul J. Steinhardt
Princeton University

The Ekpyrotic Model of the Universe proposes that our current
universe arose from a collision of two three-dimensional worlds
(branes) in a space with an extra (fourth) spatial dimension.
The proposal is interesting in and of itself, but also because
it is the precursor to a more powerful and explanatory
theory, the Cyclic Model described in earlier links on this page.

What is the Big Bang model?

To the public, the model means that the universe began from a
single point, underwent an explosion, and has been flying apart ever
since.

However, the big bang is not an explosion at all. This is an
unfortunate misnomer that cosmologists would like to correct. But
the bad name has stuck.

The big bang is the expansion or stretching of space. It is not that
things are flying out from a point. Rather, all things are moving
away from each other. It is like having an infinite rubber sheet with
people sitting on it. Stretch the rubber sheet, and all the people move away
from one another. Each things they are at the center of an explosion.
It is an optical illusion - everybody moves away from everybody
else and there is no center.

Run the story going back and time and the sheet was more and more
unstretched and the people were closer together. When everybody is
so close they are on top of one another, that is is the beginning
of the big bang picture - the cosmic singularity. At that time,
the universe has nearly infinite density and temperature.

Does the new theory contradict the Big Bang model?

Here we must be careful. There are some skeptics who have
written "the Big Bang never happened", by which they mean that the
universe is not expanding today and it never has been.
They say this despite overwhelming evidence in favor of expansion and
cooling today and for the last 15 billion years.
Our model does nothing to contradict this story. That is, the universe
has been expanding for the past 15 billion years.

What our model does is amend the earliest moments of the story.
Instead of beginning with nearly infinite temperature and density, the
universe began in a very different state - cold and nearly vacuous.
The hot expanding universe we know came as a result of collision
that brought the universe up to a large but finite temperature and
density. The rest of the story is as the Big Bang model would have it,
but the beginning is different.

Why do we need to replace the beginning of the story?

Because the Big bang model, with no amendments, would tend to
produce a universe that is highly inhomogeneous, with a warped and
curved space, and no natural mechanism for making stars, galaxies
and larger scale structures in the universe. Cosmologists have
been trying to correct these deficiencies by amending the early
history of the universe - within the first billionth billionth
billionths of s second or less. One proposal is the
"inflationary theory" of the universe, which proposes that the universe
began hot and dense, and underwent a period of hyperexpansion.
The ekpyrotic model is a new alternative, which is, in many ways,
a more radical departure from the Big Bang concept.

What is the Ekpyrotic proposal?

The model is based on the idea that our hot big bang universe
was created from the collision of two three-dimensianal worlds
moving along a hidden, extra dimension.
The two three-dimensional worlds
collide and ``stick," the kinetic energy in the collision is
converted the quarks, electrons, photons, etc., that are confined
to move along three dimensions.
The resulting temperature is finite, so the hot big bang phase begins
without a singularity.
The universe is homogeneous because the collision and initiation of
the big bang phase occurs nearly simultaneously everywhere. The
energetically preferred geometry for the two worlds is flat, so their
collision produces a flat big bang universe. According to Einstein's
equations, this means that the total energy density of the Universe
is equal to the critical density. Massive magnetic monopoles, which are
overabundantly produced in the standard big bang theory, are not
produced at all in this scenario because the temperature after collision
is far too small to produce any of these massive particles.

Quantum effects cause the incoming three-dimensional world to
ripple along the extra-dimension prior to collision so that the
collision occurs in some places at slightly different times than
others. By the
time the collision is complete, the rippling leads to
small variations in temperature, which seed
temperature fluctuations in the microwave background and the formation
of galaxies. We have shown that
the spectrum of energy density fluctuations is scale-invariant (the same
amplitude on all scales).
The production of a scale-invariant spectrum from hyperexpansion
was one of the great triumphs of inflationary theory, and here we
have repeated the feat using completely different physics.

The building blocks of the ekpyrotic theory are derived from
superstring theory.
Superstring theory requires extra dimensions for mathematical consistency.
In most formulations, 10 dimensions are required. In the mid-1990's,
Petr Horava (Rutgers) and Ed Witten (IAS, Princeton) argued that, under
certain conditions, an additional dimension opens up over a finite
interval. Six dimensions are presumed to be curled up in a microscopic ball,
called a Calabi-Yau manifold. The ball is too small to be noticed in everyday
experience, and so our universe appears to be a four-dimensional (three
space dimensions and one time dimension)
surface embedded in a five-dimensional
space-time. This five-dimensional theory, called heterotic
M-theory, was
formulated by Andre Lukas (Sussex). Ovrut
and Dan Waldram (Queen Mary
Westerfield College). According to Horava-Witten and heterotic M-theory,
particles are constrained to move on one of the
three-dimensional boundaries on either side of the
extra dimensional interval.
Our visible universe would be one of these boundaries; the other
boundary and the intervening space
would be hidden because particles and light cannot
not travel across the intervening space. Only gravity is able
to couple matter on one boundary to the other.
In addition, there can exist other three-dimensional
hypersurfaces
in the interval, which lie
parallel to the outer boundaries
and which can carry energy. These intervening
planes are called ``branes," short for membranes.
The collision that ignites the hot big bang phase of the ekpyrotic
model occurs when a three-dimensional brane is attracted to and
collides into the boundary corresponding to our visible universe.

Where does the term "ekpyrotic" come from?

The term ``ekpyrosis" means ``conflagration" in Greek, and refers to an
ancient Stoic cosmological model. According to the model, the
universe is created in a sudden burst of fire, not unlike the collision
between three-dimensional worlds in our model. The current universe
evolves from the initial fire.

Cautionary note:

As a final remark, we feel that it is important to realize that
inflationary theory is based on quantum field theory, a well-established
theoretical framework, and the model has been carefully studied and
vetted for twenty years. Our proposal is based on unproven ideas
in string theory and is brand new. While we appreciate the
enthusiasm and interest with which the paper has been received,
we would suggest some patience before promulgating these ideas in
order to leave time for us to produce some follow-up papers
that introduce additional elements and to allow
fellow theorists time for criticism and sober judgment.